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Analysis and optimal control of some solidification processes

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  • In this paper we consider a mathematical model that describes the solidification of a binary alloy. We prove some existence and uniqueness results for a regularized problem, depending on a small parameter $\epsilon$. We also analyze the behavior of the regularized solutions as $\epsilon \to 0$. Then, we consider some associated optimal control problems. We prove existence and optimality results and we present and discuss some iterative methods.
    Mathematics Subject Classification: Primary: 93C20, 35Q93, 49K20, 35A01, 35A02; Secondary: 76D05.

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